isosceles triangle means all equal sides and sum of interior angles of a triangle have to add to 180deg. if you draw a triangle with 3 equal 60 deg angles and draw a line from the top angle straight down to the bottom line, basically dividing the triangle into two even ones. then you can say the line or bisector line from the angle makes a 90deg with the bottom line across from angle the line is drawn out of. so then that makes two even and equal triangles, then the measure of the angles will be 90deg from bisector line + 60deg from angle untouched + 30deg from bisector angle = 180 degs for sum of interior angles in both triangles now proving the altitude from the base of an isosceles triangle is also the angle bisector of that angle.
